Neutron-Antineutron Oscillations from Lattice QCD

Fundamental symmetry tests of baryon number violation in low-energy experiments can probe beyond the standard model (BSM) explanations of the matter-antimatter asymmetry of the Universe. Neutron-antineutron oscillations are predicted to be a signature of many baryogenesis mechanisms involving low-scale baryon number violation. This Letter presents first-principles calculations of neutron-antineutron matrix elements needed to accurately connect measurements of the neutron-antineutron oscillation rate to constraints on $|\mathrm{\Delta }B|=2$ baryon number violation in BSM theories. Several important systematic uncertainties are controlled by using a state-of-the-art lattice gauge field ensemble with physical quark masses and approximate chiral symmetry, performing nonperturbative renormalization with perturbative matching to the modified minimal subtraction scheme, and studying excited state effects in two-state fits. Phenomenological implications are highlighted by comparing expected bounds from proposed neutron-antineutron oscillation experiments to predictions of a specific model of postsphaleron baryogenesis. Quantum chromodynamics is found to predict at least an order of magnitude more events in neutron-antineutron oscillation experiments than previous estimates based on the “MIT bag model” for fixed BSM parameters. Lattice artifacts and other systematic uncertainties that are not controlled in this pioneering calculation are not expected to significantly change this conclusion.

Figure 1

Neutron effective mass $M_n^{PJ}(t)=\ln [G_{2pt}^{PJ}(t)/G_{2pt}^{PJ}(t+a)]$ determined from point-point and point-smeared ($J=P$, $S$) two-point correlation functions. Lattice data points are shifted for visibility and compared to two-state fits (shaded bands). The asymptotic $t$ result is compatible with the nucleon mass when converted to physical units, indicating negligible discretization and finite volume effects.

Figure 2

Ratios of three-point correlation functions for operator $Q_2$ to two-point functions vs operator insertion time $\tau$ and 10 different source or sink separations $t$. Lattice data points are shifted for visibility. These data are compared to two-state fits (colored shaded bands) used to extract the ground state bare matrix elements, which are shown with statistical uncertainty for a particular value of fit ranges (horizontal bands).

Figure 3

RI-MOM “scale-independent” renormalization factors $Z^{\mathrm{SI}}$ for the operator $Q_2$. Lattice data (circles) are fit to a constant (star) plus lattice artifacts: including $\propto (ap{)}^2$ (dashed line), $\propto (ap{)}^{-2}$ (solid line), and $O(4)$-breaking (crosses) terms [33].